The generator matrix

 1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1 X^2  1  1  1  1  X  1  0  1 X^2  1  1  X
 0 X^3+X^2  0 X^2  0  0 X^2 X^3+X^2 X^3  0 X^3+X^2 X^3+X^2 X^3  0 X^2 X^2  0 X^2 X^3+X^2  0 X^3+X^2 X^3  0 X^3+X^2  0 X^2 X^2  0 X^3 X^2  0 X^3+X^2 X^3 X^2 X^3 X^2 X^3+X^2 X^3 X^3+X^2 X^3 X^2 X^2 X^3 X^3 X^2 X^3 X^2  0  0 X^2 X^2 X^3+X^2 X^3+X^2 X^2 X^3+X^2 X^3 X^3 X^3+X^2 X^2 X^2 X^3+X^2 X^2 X^3 X^2  0
 0  0 X^3+X^2 X^2  0 X^3+X^2 X^2  0 X^2  0 X^2 X^3 X^2  0 X^3+X^2 X^3 X^2 X^2 X^3  0 X^2 X^3+X^2 X^3  0  0 X^2  0 X^3+X^2 X^2 X^3+X^2 X^3 X^3 X^3 X^3  0  0 X^3+X^2 X^3 X^2  0 X^2  0 X^3+X^2 X^3+X^2  0 X^2 X^3+X^2 X^3+X^2 X^2 X^3 X^3+X^2 X^3+X^2  0 X^3 X^3 X^3+X^2 X^2  0  0 X^3 X^3 X^2  0 X^2 X^3+X^2
 0  0  0 X^3  0  0 X^3  0 X^3 X^3  0 X^3 X^3 X^3  0 X^3  0  0 X^3 X^3  0  0 X^3 X^3  0 X^3  0 X^3 X^3 X^3  0  0  0  0 X^3 X^3  0  0 X^3 X^3  0 X^3 X^3 X^3 X^3  0  0  0 X^3  0 X^3  0 X^3  0  0  0 X^3 X^3 X^3  0  0  0  0  0  0
 0  0  0  0 X^3  0 X^3 X^3 X^3 X^3 X^3  0  0  0  0 X^3 X^3  0 X^3 X^3 X^3 X^3  0  0  0  0  0  0 X^3 X^3 X^3 X^3  0 X^3 X^3  0  0 X^3 X^3  0 X^3 X^3 X^3 X^3 X^3  0  0 X^3  0  0  0  0  0 X^3 X^3  0  0 X^3  0  0  0  0  0  0 X^3
 0  0  0  0  0 X^3  0  0  0  0  0  0  0  0  0  0  0 X^3 X^3 X^3 X^3 X^3 X^3 X^3 X^3 X^3 X^3 X^3 X^3 X^3 X^3 X^3  0  0  0  0  0 X^3  0 X^3 X^3 X^3  0 X^3  0  0 X^3  0 X^3 X^3 X^3 X^3 X^3 X^3  0 X^3 X^3  0 X^3 X^3 X^3 X^3 X^3  0 X^3

generates a code of length 65 over Z2[X]/(X^4) who´s minimum homogenous weight is 60.

Homogenous weight enumerator: w(x)=1x^0+160x^60+48x^62+128x^63+599x^64+256x^65+464x^66+128x^67+198x^68+55x^72+10x^76+1x^120

The gray image is a linear code over GF(2) with n=520, k=11 and d=240.
This code was found by Heurico 1.16 in 4.88 seconds.